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Pick representative albums from either end of Leandro “Gato” Barbieri’s sprawling career, and they may seem at first to be scarcely acquainted, much less blood relations.

But amid the wildly evolving styles of his different bands, the connective tissue has been the tenor saxophonist’s distinctive sound — marked by insistent phrasing and a robust tone, one that hints at layers of scar tissue hidden beneath a passionate, even amorous, surface.

“The jazz musicians and the people who listen to the records don’t consider me a jazz player. Because what I did was more of a lullaby to Latin America,” he says on the phone from his home in New York, “because I play everything — tangos, boleros, and some things I invent in the moment — but I never played like a tango player.”

Known for his ever-present sunglasses, wide-brimmed fedora, and affectionate nickname (Spanish for “the cat,” as well as a kind of Argentine folk dance), the 80-year-old tenor player progressed from big-band ensembles to shrieking free jazz, to his essential early-1970s work melding South American and Caribbean textures, before his taste for pop tunefulness led him to probe the slightly spicier regions within smooth jazz in the ’80s and beyond.

Gato Barbieri

English is Barbieri’s third language (after Spanish and Italian), and he speaks it haltingly. In recent years his eyesight has dimmed, and he says his memory has grown “a bit sloppy” as well. But he’s quick to recall his experiences working in the studio with Don Cherry, the trumpeter and Ornette Coleman collaborator who first turned Barbieri’s gaze away from inherited jazz traditions.

“I always played bebop until I played with Don Cherry and everything changed. He was incredible. He was between free jazz and something else,” Barbieri says, adding that Cherry would give his band spare instructions, but be specific about time and tempo changes. “I learned from him to listen to the leader. And since then I am a good leader because I don’t say too much. I play, and you have to feel what I do.”

Barbieri moved from the Argentine provinces to Buenos Aires as a teenager, emerging in the orchestra of countryman Lalo Schifrin. The Cherry influence came after Barbieri’s move to Italy in 1962, where the two met and the saxophonist was drafted into sessions for influential free jazz records like “Symphony for Improvisers.” His first session as a leader, “In Search of the Mystery” in 1967, is a bracing blast of the free stuff. His horn work is almost unrelenting in its intensity, but deeply affecting. No emotionally blank exercise in chopsmanship, this.

The musical interests of his next several decades commingled two years later on “The Third World,” where he mixed and matched elements of the free approach with a sort of proto-world-music, and a sensitivity on the horn fit for a tender ballad.

Describing the constant element flowing through his work, Barbieri cites an example from the world of cinema.

“Hitchcock made a lot of films but he always has his own point of view. He didn’t always do the same thing, but it was the same feeling,” he says. “My point is: me, too.”

It was his much-loved score for a film, “Last Tango in Paris” in 1972, that raised his profile and launched a prolific compositional sideline. A break toward more commercial fare was on the horizon, but not before he finished a series of highly focused albums, recorded mostly in Buenos Aires, New York City, and Rio de Janeiro, that wove folk styles of South America with Afro-Caribbean influences and the chic urbanity of American jazz.

“He used a lot of rhythms from down south, a lot of stuff from Bolivia and Argentina. At the time, people were not prepared to hear that,” observes Oscar Stagnaro, a Latin music specialist on the faculty of Berklee College of Music who’s won four Grammys while playing bass with Cuban bandleader Paquito D’Rivera. “He changes styles, but his sound — you hear one note and you know that’s Gato.”

The slick production and mellow tones of later albums, in the mid-’70s and later, achieved crossover success but left little to fascinate purists. He slowed down significantly in the ’90s after the twin misfortunes of the death of his longtime wife, Michelle, and his emergency triple-bypass surgery six weeks later.

But he’s continued to work sporadically, and the 2002 effort “The Shadow of the Cat” was named the best Latin jazz album of the year by Billboard. His 2011 standards record “New York Meeting” marks another left turn; the stripped-down, elegant affair is the most post-bop-informed album he’s made in decades, if not ever.

Material aside, he says, his focus is still the sound on his tenor.

“I’ve played 60 years! And now I am in the moment where I can play very well. I don’t have too much new stuff, it’s about how I play. I play the same tunes but they are different.”

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